The use of rewriting systems to transform a given expression into a simpler one has promoted the use of rewriting logic in several areas and, particularly, in Software Engineering. Unfortunately, this application has not reached the treatment of Functional Dependencies contained in a given relational database schema. The reason is that the different sound and complete axiomatic systems defined up to now to manage Functional Dependencies are based on the transitivity inference rule. In the literature, several authors illustrate different ways of mapping inference systems into rewriting logics. Nevertheless, the explosive behavior of these inference systems avoids the use of rewriting logics for classical FD logics. In a previous work, we presented a novel logic named SLFD whose axiomatic system did not include the transitivity rule as a primitive rule.
In this work we consider a new complexity criterion which allows us to introduce a new minimality property for FD sets named atomic-minimality. The SLFD logic has allowed us to develop the heart of this work, which is the use of Rewriting Logic and Maude 2 as a logical framework to search for atomic-minimality.